Problem: Simplify the following expression: $y = \dfrac{a^2 + 8a + 15}{a + 5} $
Answer: First factor the polynomial in the numerator. $ a^2 + 8a + 15 = (a + 5)(a + 3) $ So we can rewrite the expression as: $y = \dfrac{(a + 5)(a + 3)}{a + 5} $ We can divide the numerator and denominator by $(a + 5)$ on condition that $a \neq -5$ Therefore $y = a + 3; a \neq -5$